this reduction ought to be made by calculation,* or at least by reference to tables of reduction of hypothenusal lengths to horizontal ones as given below.

Tables of reduction are engraved on the vertical arc of Theodolites which, while they show on one side the angle of elevation or depression, give on the other the number of units per hundred, that have to be deducted to reduce the hypothenusal line to its corresponding horizontal length.

*This calculation is simple: Suppose AC to represent the horizontal plane, and AB the measured line; the angle of elevation BAC being taken with the Theodolite, we have the side AB, the angle BAC, and the angle BCA,

a right angle, to find the line AC, which is the horizontal length required.

B

In small Surveys, especially those made with the Chain only, an allowance or reduction is generally made in the field by construction or estimation as the measurement proceeds. If the slope be not very steep, the reduction is accomplished by holding the lower end of the Chain above the ground, as nearly horizontal as can be judged by the eye, allowing a plummet to hang from the hand that holds the Chain, in order to point, to where the arrow should be placed.

When perfect accuracy, however, is sought, and when the Survey is extensive, the angles of inclination should be observed, and the proper deduction obtained by computation, and allowed for when the work is being plotted.

CHAPTER VI.

ON THE TRAVERSE SYSTEM AND GALE'S METHOD OF SURVEYING.

A TRAVERSE may be defined as a circuitous route performed on leaving any place on the earth's surface, by stages, in different directions, and of various lengths, with a view of arriving at any other place situated in any direction with reference to the former, and at any distance therefrom which cannot be reached in the direction of the shortest line connecting them. The angles which the stages or station lines form with the meridian are called "bearings" the quantity of Northing or Southing made in each distance, is called the difference of latitude, and the amount of Easting or Westing is termed the departure.

When the bearing corresponds with the meridian, or with the perpendicular to it, there will in the former case be no difference of latitude, and in the latter no departure, and the distance measured will itself express the amount of Northing or Southing, or of Easting or Westing due to the change of position.

When, however, the bearing does not correspond with the meridian or with the perpendicular to it, there will be for every distance measured a certain corresponding change both in latitude and longitude (or departure); and as these will with

reference to their particular distance answer the condition of our definition, they may with propriety be termed the traverses of the distances:

We will therefore define:

1st. Meridians as North and South lines, which are supposed to pass through every station of a Survey, running parallel to each other.*

2nd. The difference of latitude or the Northing or Southing of any line, as the distance that one end of a line is North or South from the other end.

3rd. The departure of any line, as the perpendicular distance from one end of the line to a meridian passing through the other end.

In the 3rd Cor. Theor. V., (page 12,) it is stated and proved, "that all the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides" or in other words that—

In any rectilineal figure, the sum of all the interior angles, is equal to twice as many right angles as the figure has sides, less four right angles.

This forms the basis on which the Revenue Survey operations in India are conducted. The Traverse System is a method of computation by rectangular co-ordinates, and is applicable to any mode of surveying, whatever, such as Route Surveys, Railway Lines, Navigation Courses and the like, where every Station is fixed by distances on the meridian and perpendicular, and this is essential to Gale's System, which may be termed the periphery measuring or perimetrical method. By throwing a series of angles over the face of a country, and forming a network of large circuits, the liability of error is reduced within the narrowest limits, which the means at

* These meridians are not really parallel, but converge towards the poles of the earth, but so insensibly as not to be worthy the notice of a Surveyor's operations within a limited space.

disposal permit. This angular Circuit System, in extensive operations in a country like India, with instruments of the best construction and moderate power and size, can alone enable a Surveyor to carry out in practice the theoretical accuracy of the Traverse, and permit by the aid of logarithmic calculation an approximation to the proof required, viz. :

1st. "That the sums of all the interior angles shall be equal to twice as many right angles as the figure has sides, less four right angles" and—

2nd. As regards the linear measurements," That the sums of the Northings be equal to the sums of the Southings, and the sums of the Eastings be equal to the sums of the Westings, which latter will be presently explained.

It is not intended to be advanced that the Indian System will bear comparison with the Ordnance Survey of Great Britain, as respects the Geometrical principles, on which they are respectively based. The latter is on a Trigonometrical basis throughout, and the errors in detail have never reached the assigned limits of of superficial or of linear measure. The periphery measurement system of India is not capable of giving results so accurate as the Ordnance Survey System, because a space is not rigorously represented by its perimeter, at the same time where boundaries are the chief object of the Survey, the simplicity of the latter system, is an immense advantage, and considering the expenditure of time and money the results of the Indian System are admirable. The country could not possibly be surveyed so economically, or so rapidly in any other way, and bearing in mind the relative value of ground in the two countries it would not be advisable to adopt the more expensive and more accurate system of the Ordnance Survey, it would in fact be an endless job in such a vast empire, a complete first Survey likewise, being most urgently needed.

Hutton in speaking of the Traverse Table, observes" that this mode of surveying large tracts of lands was made use of